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What is the remainder when 2 + 4 + 6 + ... + 100 + 102 + 104 is divided by 7?

 Jul 4, 2021
 #1
avatar+33606 
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Arithmetic sequence with 52 terms

 

sum = 52 ( 2+104)/2 =2756                2756 mod 7 =5

 Jul 4, 2021
 #2
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0

There are 52 terms in the sequence. If you divide each of the numbers in 2: 2,4,6,...,102,104 = 1,2,3,...,51,52.

2+104 = 4+102 = 6+100 which means ((2+104)x52)/2 equals the sum of the sequence, which is 2756, and if you divide that by 7 you get 393 r5.

So, the answer is 5. 

 Jul 4, 2021

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